Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications: In Honor of Professor Raytcho Lazarov's 40 Years of Research in Computational Methods and Applied Mathematics

333 Pages·2013·3.62 MB·English

by  J. H. Adler

Springer Proceedings in Mathematics & Statistics
Oleg P. Iliev · Svetozar D. Margenov
Peter D. Minev · Panayot S. Vassilevski
Ludmil T. Zikatanov Editors
Numerical Solution
of Partial Diff erential
Equations: Theory,
Algorithms, and
Their Applications
In Honor of Professor Raytcho Lazarov’s
40 Years of Research in Computational
Methods and Applied Mathematics
Springer Proceedings in Mathematics & Statistics
Volume 45
Forfurthervolumes:
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mathematicalandstatisticalresearchtoday.
Oleg P. Iliev • Svetozar D. Margenov
Peter D. Minev • Panayot S. Vassilevski
Ludmil T. Zikatanov
Editors
Numerical Solution of Partial
Differential Equations:
Theory, Algorithms, and
Their Applications
In Honor of Professor Raytcho Lazarov’s 40
Years of Research in Computational Methods
and Applied Mathematics
123
Editors
OlegP.Iliev SvetozarD.Margenov
DepartmentofFlowandMaterial InstituteforParallelProcessing
Simulation BulgarianAcademyofSciences
FraunhoferInstitute Sofia,Bulgaria
forIndustrialMathematics
Kaiserslautern,Germany PanayotS.Vassilevski
CenterforAppliedScientific
PeterD.Minev Computing
DepartmentofMathematicaland LawrenceLivermoreNational
StatisticalSciences Laboratory
UniversityofAlberta Livermore,CA,USA
Edmonton,AB,Canada
LudmilT.Zikatanov
DepartmentofMathematics
ThePennsylvaniaStateUniversity
UniversityPark,PA,USA
ISSN2194-1009 ISSN2194-1017(electronic)
ISBN978-1-4614-7171-4 ISBN978-1-4614-7172-1(eBook)
DOI10.1007/978-1-4614-7172-1
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2013939589
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Preface
Thedesignandimplementationofnumericalmodelsthataccuratelycapturetheap-
propriatemodelfeaturesofcomplexphysicalsystemsdescribedbytime-dependent
coupledsystems of nonlinearPDEs presentone of the main challengesin today’s
scientific computing. This volume integrates works by experts in computational
mathematics, and its applications focused on the modern algorithms which are
in the core of accurate modeling: adaptive finite-element methods, conservative
finite-difference and finite-volume methods, and multilevel solution techniques.
Fundamentaltheoreticalresultsarerevisitedinseveralsurveyarticles,andnewtech-
niques in numerical analysis are introduced. Applications showing the efficiency,
reliability,androbustnessofthealgorithmsinporousmedia,structuralmechanics,
andelectromagnetismarepresented.
The volume consists of papers prepared in the context of the International
Symposium “Numerical Solution of Partial Differential Equations: Theory, Algo-
rithmsandtheirApplications”inhonorofProfessorRaytchoLazarov’s40yearsof
researchincomputationalmethodsandappliedmathematicsandontheoccasionof
his70thbirthday.
The symposium was organized and sponsored by the Institute of Information
andCommunicationTechnologies(IICT),BulgarianAcademyofSciences(BAS),
LawrenceLivermoreNationalLaboratory(USA),andDepartmentofMathematics,
ThePennsylvaniaStateUniversity(USA).Membersoftheprogramcommitteeare
OlegIliev(ITWMFraunhofer,Kaiserslautern,Germany),PeterMinev(University
of Alberta, Canada), Svetozar Margenov (Institute of Information and Commu-
nication Technologies, BAS), Panayot Vassilevski (Lawrence Livermore National
Laboratory, USA), and Ludmil Zikatanov (The Pennsylvania State University,
USA).
Thelistofparticipantswhowereinvitedtocontributeandauthoredorcoauthored
apaperincludedinthisvolumeis:
Owe Axelsson(UppsalaUniversity,Sweden;KAU, SaudiArabia;Academyof
Sciences,CzechRepublic)
CarstenCarstensen(HumboldtUniversityofBerlin,Germany)
v
vi Preface
PanagiotisChatzipantelidis(UniversityofCrete,Greece)
IvanDimov(IICT,BulgarianAcademyofSciences,Bulgaria)
StefkaDimova(SofiaUniversity,Bulgaria)
OlegIliev(ITWMFraunhofer,Germany)
UlrichLanger(JohannesKeplerUniversityandRICAM,Austria)
SvetozarMargenov(IICT,BulgarianAcademyofSciences,Bulgaria)
PeterMinev(UniversityofAlberta,Canada)
JosephPasciak(TexasA&M,USA)
PetrVabishchevich(IMM,RussianAcademyofSciences,Russia)
PanayotVassilevski(LawrenceLivermoreNationalLaboratory,USA)
JunpingWang(NationalScienceFoundation,USA)
JoergWillems(RICAM,AustrianAcademyofSciences,Austria)
LudmilZikatanov(ThePennsylvaniaStateUniversity,USA)
The editors are grateful to the Institute of Information and Communication
Technologies (IICT), Bulgarian Academy of Sciences, the Lawrence Livermore
National Laboratory, and the Department of Mathematics at Penn State for the
supportofthesymposium.
Onbehalfofallthecontributors,wededicatethisvolumetoourteacher,friend,
andcolleagueRaytchoLazarov.
Kaiserslautern,Germany OlegP.Iliev
Sofia,Bulgaria SvetozarD.Margenov
Edmonton,AB,Canada PeterD.Minev
Livermore,CA,USA PanayotS.Vassilevski
UniversityPark,PA,USA LudmilT.Zikatanov
Preface vii
Onthe Occasionof the70th Anniversaryof RaytchoLazarov
With great pleasure we introduce this collection of papers in honor of Raytcho
Lazarov,professorattheTexasA&MUniversityandDoctorofSciencesandDoctor
HonorisCausaofthe“St.KlimentOhridski”UniversityofSofia,Bulgaria.
Raytcho Lazarov is a computational mathematician of extraordinary depth
and breadth whose work has had and continues to have exceptional impact on
computationalandappliedmathematics.Hehasauthoredorcoauthoredmorethan
200 journal publications and 4 books spanning all major areas in computational
mathematics and bridging mathematical theory and scientific computing with
sciencesandengineering.
RaytchoLazarovwasborninKardzhali( ),Bulgaria,onJanuary23,
1943.Hegraduatedfrom“St.AntimI”High(cid:0)S(cid:2)ch(cid:3)o(cid:4)o(cid:5)l(cid:6)in(cid:7)Z(cid:8)latograd( )and
in 1961 went to Sofia University “St. Kliment Ohridski” to con(cid:9)tin(cid:7)u(cid:6)e(cid:10)(cid:11)h(cid:12)i(cid:3)s(cid:6)s(cid:4)tudies
in the Department of Mathematics (industrial profile). During his first year as a
collegestudent,Raytchodemonstratedhistalentformathematics,andhisdedication
to study it, and he was selected to continue his education at the University of
Wroclaw in Poland in 1963. In Wroclaw Raytcho was able to interact with many
distinguished mathematicians from the Polish mathematical school and received
first-ratemathematicaltraining.
In1968RaytchoLazarovwasadmittedtothePhDprogramoftheMoscowState
University. As a graduate student in Moscow, he studied and worked under the
supervisionofAcademicianA.A.Samarskiiwhowasoneofthebestcontemporary
computationalmathematiciansin the world. Lazarov’sthesis workwas on “Finite
differenceschemesforelasticityproblemsincurvilineardomains,”amongthefirst
rigorousstudiesofnumericalapproximationsofproblemsinstructuralmechanics.
AfterreceivinghisPhDdegreein1972,RaytchoLazarovworkedasaresearch
associate andseniorresearchassociate in theInstitute ofMathematics(IM)ofthe
BulgarianAcademyofSciences(BAS)until1987.Duringthistimeheestablished
himself as one of the leading experts in numerical analysis. In 1976 Raytcho
Lazarov visited the Rutherford Laboratory in Didcot, UK, for one year, and this
visithadnotableimpactonhisfutureresearch.Hisfocusshiftedtothetheoryand
applicationsof the finite elementmethod (FEM) which remainsto be his primary
fieldofresearchtothisday.
Lazarov earned the degree of doctor of sciences in June 1982 with a thesis on
“Error estimates of the difference schemes for some problems of mathematical
physics having generalized solutions.” This thesis contained several breakthrough
results, which were published in more than 10 papers and formed the basis for
a research monograph that he coauthored with A. A. Samarskii and V. Makarov,
Difference Schemes for Differential Equations Having Generalized Solutions,
whichwaspublishedin1987.
In 1986 Lazarov’s superb scientific achievements earned him the title of a
professorofmathematicsattheInstituteofMathematicsoftheBulgarianAcademy
ofSciences, a positionthathe continuesto hold to thisday.His leadershipability
viii Preface
was also recognized by his colleagues, and in 1985 he became the head of the
Laboratoryon NumericalAnalysis, BAS, and a deputy-directorof the Laboratory
on Parallel Algorithms and High Performance Computer Systems, BAS. In 1986
Lazarov became deputy-director of the newly established Center for Informatics
andComputerTechnology(CICT)atBAS.Thiswasoneofthefirstinterdisciplinary
centersworldwideformathematicalresearchonadvancedalgorithmsfortheemerg-
ing parallel computer systems. He played a crucial role in hiring a cohort of the
best young applied mathematicians in Bulgaria—Djidjev, Vassilevski, Margenov,
Dimov, Bochev, and many more. In fact, Raytcho Lazarov’s leadership was the
keyinmakingCICToneofthebestplacesforlarge-scalescientificcomputingand
parallelalgorithms.In1984Raytchoinitiatedaseriesofinternationalconferences
onnumericalmethodsandapplicationsinSofia,Bulgaria,whichhelpedtopublicize
the results and achievements of the Bulgarian numerical analysts and to integrate
themintotheinternationalcommunity.
Such accomplishmentswere noticedby hiscolleaguesaroundthe world. Vidar
Thome´ehelpedRaytchotogetavisitingpositionattheUniversityofWyomingin
1987.ThisturnedouttobeacriticalpointinLazarov’scareer.InWyominghemet
andbefriendedRichardEwingwhoatthattimewasadirectoroftheEnhancedOil
RecoveryInstitute(EORI)andtheInstituteofScientificComputation(ISC) atthe
UniversityofWyoming.DuringhisstayinLaramiein1988–1992,Lazarovworked
onsuperconvergenceandlocalrefinementtechniquesformixedFEmethods.During
that time Raytcho initiated many collaborations and friendships with prominent
mathematicians such as Jim Bramble, Joe Pasciak, Panayot Vassilevski, Junping
Wang,TomRussell,YuriKuznetsov,SteveMcCormick,TomManteuffel,andOwe
Axelsson. At that time Raytcho Lazarov led the developmentof algorithmsbased
ontheBramble–Ewing–Pasciak–Schatz(BEPS)preconditionerandlocallyrefined
mixed FE and finite-volume methods that were also implemented in the EORI
proprietarycodes.
The friendship and collaboration with Dick Ewing initiated another change in
Raytcho’scareer, and in 1992he movedto Texas A&M University as a professor
of mathematics, a position that he continues to hold now. This coincided with
the establishment of the Institute of Scientific Computation (ISC) at Texas A&M
underthedirectorshipofRichardEwing,whichquicklyattractedateamofworld-
renowned experts in this area like J. Bramble, J. Pasciak, R. Lazarov, and, more
recently, Y. Efendiev, J.-L. Guermond, G. Petrova, B. Popov, W. Bangerth, and
A. Bonito. The work they did in the last 20 years on computational mathematics
and its applications in flows in porous media, multiphysics problems, modeling
of fluids, structures and their interactions, etc. had a significant impact on these
and in other research areas. Raytcho’s pivotal role in this research is well known
fromhisresultsonleast-squaresFEM;discontinuousGalerkinmethods;multigrid,
multilevel,andmultiscalemethods,mixedFEM,andmorerecentlyfractionalorder
partialdifferentialequations.
In recognition of his achievements Raytcho Lazarov has been awarded several
honorarytitlesanddegrees:the medal“St. Kl.Ohridski”with blueribbon(2003–
thehighesthonorsgivenbySofiaUniversity,Bulgaria,toscientists);DoctorHonoris
Preface ix
Causa of Sofia University “St. Kl. Ohridski” (2006); the medal of the Institute
of Mathematics, Bulgarian Academy of Sciences 2008; Pichoridis Distinguished
Lectureship, University of Crete, Greece (2008); and Erasmus Mundus Visiting
Scholar Award, University of Kaiserslautern (2008).Most recently he was named
a recipient of the medal of the Bulgarian Academy of Sciences “Marin Drinov”
withribbon(2013),whichisgiventoscholarsforoutstandingcontributionsinthe
advancementofscience.
DuringhiscareerLazarovhasheldvisitingpositionsandcontributedtoadvance-
mentofresearchin manyinstitutionsaroundthe globe:JointInstitute forNuclear
ResearchinDubna,Russia(1980);AustralianNationalUniversity,Canberra(1990);
Mittag Leffler Institute of Mathematics, Stockholm, Sweden (1998); University
of Linz and RICAM, Austria (2005); Fraunhofer Institute of Industrial Mathe-
matics,Kaiserslautern,Germany(2006);LawrenceLivermoreNationalLaboratory
(regularly from 1998 to 2010); and KAUST in Saudi Arabia (2008–2013).He is
a member of the editorial board of five international journals and a number of
conference proceedings, and he is also serving on the scientific committees of
severalinternationalconferences.
RaytchoLazarovisanoutstandingscholar,andhisworkhashadaprofoundim-
pactonmathematicsandotherfieldsofscienceandengineeringduringthelastfour
decades.Hisextraordinarypersonality,withstrictacademicintegrityrequirements
forhimselfandhiscollaboratorscomplementedbytrulycompassionatecareabout
theirneeds,hasinfluencedtheprofessionalandpersonaldevelopmentofthosewho
have had a chance to work with him. The teams which he has created over the
years combined research interests, philosophy, and personal friendship, and they
withstoodthetestoftime.
WecongratulateRaytchoontheoccasionofhis70thbirthdayandwishhimthe
bestof healthandenjoymentin his personallife andin continuingandexpanding
hissuccessfulresearchachievements.
Kaiserslautern,Germany OlegP.Iliev
Sofia,Bulgaria SvetozarD.Margenov
Edmonton,AB,Canada PeterD.Minev
Livermore,CA,USA PanayotS.Vassilevski
UniversityPark,PA,USA LudmilT.Zikatanov